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WEIGHTED ESTIMATES FOR SINGULAR INTEGRAL OPERATORS WITH NONSMOOTH KERNELS AND APPLICATIONS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 85 / Issue 3 / December 2008
- Published online by Cambridge University Press:
- 01 December 2008, pp. 377-417
- Print publication:
- December 2008
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- Article
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Let 𝒳 be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, two weighted estimates related to
weights are established for singular integral operators with nonsmooth kernels via a new sharp maximal operator associated with a generalized approximation to the identity. As applications, the weighted Lp(𝒳) and weighted endpoint estimates with general weights are obtained for singular integral operators with nonsmooth kernels, their commutators with BMO (𝒳) functions, and associated maximal operators. Some applications to holomorphic functional calculi of elliptic operators and Schrödinger operators are also presented.
weights are established for singular integral operators with nonsmooth kernels via a new sharp maximal operator associated with a generalized approximation to the identity. As applications, the weighted 